Collisions
Use H1 Physics impulse and momentum conservation to analyse collisions, distinguish elastic behaviour and calculate kinetic-energy transfers.
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Before you begin
In a collision the forces are large, short and hard to measure, yet the outcome can still be predicted. The lessons start with impulse, the area under a force–time graph, which equals the change in momentum. They then use Newton’s third law to show that the total momentum of colliding bodies is conserved, solve perfectly elastic collisions, and finish by working out how much kinetic energy a collision transfers to other stores.
Be comfortable with: linear momentum, because every collision calculation uses it, and kinetic energy.
Learning goals
- Use impulse and momentum conservation in one-dimensional elastic and inelastic collisions.
Syllabus statements covered
- recall that impulse is given by the area under the force-time graph for a body and use this to solve problems
- state the principle of conservation of momentum
- apply the principle of conservation of momentum to solve simple problems including inelastic and (perfectly) elastic interactions between two bodies in one dimension (knowledge of the concept of coefficient of restitution is not required)
- show an understanding that, for a (perfectly) elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation
- show an understanding that, whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place
Lessons
Work through them in order.
- Impulse and force–time areaFind impulse as the area under a force–time graph, use it as the change in momentum, and explain why a longer impact time reduces the force.
- Conservation of momentum in interactionsState the principle of conservation of momentum and use it to solve one-dimensional collisions, including bodies that stick together.
- Perfectly elastic collisionsUse conservation of momentum and the equal relative speeds of approach and separation to find both velocities after a perfectly elastic collision.
- Kinetic-energy change in collisionsExplain why momentum is conserved while kinetic energy usually is not, and calculate the kinetic energy transferred in a collision.
Practise and check
Or choose
Topic reference
Quick reference
| Idea | Relationship | Note |
|---|---|---|
| impulse | FΔ t = Δ p; area under a force–time graph | unit N s = kg m s⁻¹ |
| average force | F = (Δ p)/(Δ t) | longer time, smaller force |
| conservation of momentum | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | no resultant external force |
| bodies that stick | m₁u₁ + m₂u₂ = (m₁ + m₂)v | kinetic energy always lost |
| perfectly elastic collision | u₁-u₂ = v₂-v₁ | kinetic energy conserved |
| kinetic energy transferred | E_(k,before)-E_(k,after) | add (1/2)mv² for every body |
Core knowledge to remember
- Impulse is given by the area under the force–time graph for a body, and is equal to its change in momentum.
- Principle of conservation of momentum: the total momentum of a system of interacting bodies remains constant, provided no resultant external force acts on the system.
- Momentum is conserved because the bodies exert equal and opposite forces on each other for the same time (Newton’s third law).
- In a perfectly elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation, and kinetic energy is conserved.
- Whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place. In an inelastic collision, kinetic energy is transferred to internal energy and sound.
Common mistakes
- Multiplying the peak force by the whole contact time instead of finding the area under the force–time graph.
- Saying an airbag reduces the change in momentum, rather than the force.
- Applying conservation of momentum to each body separately, or losing the sign of a velocity.
- Assuming kinetic energy is conserved because momentum is.
- Adding speeds to find a relative speed when both bodies move the same way.